LEADER 04249nam 2200589 450 001 9910807394603321 005 20170822144155.0 010 $a1-4704-0327-7 035 $a(CKB)3360000000464918 035 $a(EBL)3114461 035 $a(SSID)ssj0000973186 035 $a(PQKBManifestationID)11523482 035 $a(PQKBTitleCode)TC0000973186 035 $a(PQKBWorkID)10960087 035 $a(PQKB)10685380 035 $a(MiAaPQ)EBC3114461 035 $a(RPAM)12403274 035 $a(PPN)195416201 035 $a(EXLCZ)993360000000464918 100 $a20010509d2001 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBlowing up of non-commutative smooth surfaces /$fMichel Van den Bergh 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2001. 215 $a1 online resource (157 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 734 300 $a"November 2001, volume 154, number 734 (end of volume)." 311 $a0-8218-2754-5 320 $aIncludes bibliographical references (pages 139-140) and index. 327 $a""Contents""; ""Chapter 1. Introduction""; ""1.1. Motivation""; ""1.2. Construction""; ""1.3. General properties""; ""1.4. Non-commutative Del-Pezzo surfaces""; ""1.5. Exceptional simple objects""; ""1.6. Non-commutative cubic surfaces""; ""1.7. Acknowledgement""; ""Chapter 2. Preliminaries on category theory""; ""Chapter 3. Non-commutative geometry""; ""3.1. Bimodules""; ""3.2. Graded modules, bimodules and algebras""; ""3.3. Quotients of the identity functor""; ""3.4. Ideals in the identity functor""; ""3.5. Quasi-schemes""; ""3.6. Divisors""; ""3.7. Proj"" 327 $a""3.8. Condition ""X"" and cohomological dimension""""3.9. Higher inverse images""; ""3.10. Algebras which are strongly graded modulo a Serre subcategory""; ""3.11. The positive part of certain graded algebras""; ""3.12. Veronese subalgebras""; ""Chapter 4. Pseudo-compact rings""; ""Chapter 5. Cohen-Macaulay curves embedded in quasi-schemes""; ""5.1. Preliminaries""; ""5.2. Some computations""; ""5.3. Completion of objects in mod(X)""; ""5.4. Completion of bimodules""; ""5.5. The category C[sub(f,p)]""; ""5.6. Completion of algebras"" 327 $a""5.7. Multiplicities in the case that I?? has infinite order""""Chapter 6. Blowing up a point on a commutative divisor""; ""6.1. Some ideals""; ""6.2. Some Rees algebras""; ""6.3. Definition of blowing up""; ""6.4. The normal bundle""; ""6.5. Birationality""; ""6.6. The exceptional curve""; ""6.7. The structure of the exceptional curve""; ""6.8. The strict transform""; ""6.9. A result on K[sub(0)] of some categories""; ""Chapter 7. Derived categories""; ""7.1. Generalities""; ""7.2. Admissible compositions of morphisms between quasi-schemes"" 327 $a""Chapter 8. The derived category of a non-commutative blowup""""8.1. The formalism of semi-orthogonal decompositions""; ""8.2. Generalities""; ""8.3. Computation of some derived functors""; ""8.4. The main theorem""; ""Chapter 9. Some results on graded algebras and their sections""; ""9.1. Generalities""; ""9.2. The case of a blowing up""; ""Chapter 10. Quantum plane geometry""; ""10.1. Multiplicities of some objects""; ""10.2. Classification of lines and conics""; ""Chapter 11. Blowing up n points in an elliptic quantum plane""; ""11.1. Derived categories"" 327 $a""11.2. Exceptional simple objects""""Chapter 12. Non-commutative cubic surfaces""; ""Appendix A. Two-categories""; ""Appendix B. Summary of notations""; ""Appendix C. Index of terminology""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 734. 606 $aNoncommutative differential geometry 606 $aBlowing up (Algebraic geometry) 615 0$aNoncommutative differential geometry. 615 0$aBlowing up (Algebraic geometry) 676 $a510 s 676 $a516.3/6 700 $aBergh$b M. van den$01683486 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807394603321 996 $aBlowing up of non-commutative smooth surfaces$94054259 997 $aUNINA